Question: Solve for $x$ and $y$ using elimination. ${6x-4y = -18}$ ${-5x-3y = -23}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $3$ and the bottom equation by $-4$ ${18x-12y = -54}$ $20x+12y = 92$ Add the top and bottom equations together. $38x = 38$ $\dfrac{38x}{{38}} = \dfrac{38}{{38}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {6x-4y = -18}\thinspace$ to find $y$ ${6}{(1)}{ - 4y = -18}$ $6-4y = -18$ $6{-6} - 4y = -18{-6}$ $-4y = -24$ $\dfrac{-4y}{{-4}} = \dfrac{-24}{{-4}}$ ${y = 6}$ You can also plug ${x = 1}$ into $\thinspace {-5x-3y = -23}\thinspace$ and get the same answer for $y$ : ${-5}{(1)}{ - 3y = -23}$ ${y = 6}$